Length across cuboid at an angle

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I would like to calculate the change in length across a cuboid when looking at it from different angles (e.g. 10 and 20°).

In the illustration below the red arrows show the length I would like to calculate. Ideally, I would like to have an average of all the lengths across the cuboid. The aspect ratio between the width and length of the cuboid would be quite large (around 30).

Illustration cuboid at different angles



What equation would you suggest?

Please do not hesitate if there is anything unclear.

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From the perspective of the cuboid, it looks like this:

enter image description here

When the cuboid is rotated by some angle $\theta$, $\cos \theta = \frac{\text{adjacent side}}{\text{hypotenuse}}$, so the rotated length will be equal to $\cos \theta$ multiplied by the width of the cuboid.